This is a consequence of the relative Levinson's theorem, see [1]}. This general statement is true for any continuous parameter in a compact domain, such as \(\theta \) . As \(\kappa \rightarrow 0\)  the scattering amplitude is computed near the bottom of the upper band, and feels the bound states below it. As \(\theta \)  increases, it then counts the change in the number of bound states, that is the number of edge modes from the definition above. We illustrate it for specific values of R in Figure REF .
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